As a simple model, suppose you arrange for the intense bleaching pulse of light to illuminate
a cell in a pattern of parallel planes. That is, immediately after bleaching (at time t=0), the
remaining fluorescence intensity Θ(x) has the form Θ(x)= C(i) + C(1)sin(2pix/L) where the two C terms are constants with C(0) greater than C(1). The constant L is the periodicity of the bleach pattern. A. Show that the mean fluorescence intensity immediately after bleaching equals C(0). B. At later times, the fluorescence intensity has the form Θ(x)= C(0) + Δ(t)sin(2pix/L). Derive an expression for the diffusion constant D of the fluorescent molecules in terms of the measured quantity Δ(t). Assume that the region of interest is sufficiently small that you can approximate the cell as having infinite volume.
Homework Equations1D diffusion equation perhaps?
The Attempt at a Solutionobeys the 1D diffusion equation as the instructor told us this.
We only need to calculate within 1 period, from 0 to L.